Understand the rule first
Identify the scale and units before using the data. Mean is total ÷ number of values; range is largest − smallest.
Data, averages & range 11+ practice
Read data carefully and calculate mean, range and comparisons from the correct values.
Find the mean and range of 6, 8, 8, 13, 15.
- Total: 6 + 8 + 8 + 13 + 15 = 50.
- Mean: 50 ÷ 5 = 10.
- Range: 15 − 6 = 9.
A common misconception
Dividing by the largest value instead of by the number of values when finding a mean.
Reusable method: Check whether a graph scale increases in ones, twos, fives or another interval.Question 1 of 10 MathscoreWhat is the range of 14, 9, 21, 16 and 12?
- A7
- B9
- C12
- D30
Need a hint?
Subtract the smallest value from the largest.
Show worked answer
Answer C: 12
21 − 9 = 12.
Quick method: Check whether a graph scale increases in ones, twos, fives or another interval.
Question 2 of 10 MathscoreThe mean of four scores is 18. What is their total?
- A4.5
- B22
- C54
- D72
Need a hint?
Reverse total ÷ number by multiplying.
Show worked answer
Answer D: 72
Total = mean × number of scores = 18 × 4 = 72.
Quick method: Check whether a graph scale increases in ones, twos, fives or another interval.
Question 3 of 10 MathscoreFind the mean of 7, 11, 12 and 18.
- A10
- B11
- C12
- D13
Need a hint?
Add the four values and divide by four.
Show worked answer
Answer C: 12
7 + 11 + 12 + 18 = 48; 48 ÷ 4 = 12.
Quick method: Check whether a graph scale increases in ones, twos, fives or another interval.
Question 4 of 10 Mathsexam-styleFive numbers have a mean of 16. Four are 12, 15, 17 and 21. What is the fifth number?
- A13
- B15
- C16
- D80
Need a hint?
Find the required total, then subtract the four known values.
Show worked answer
Answer B: 15
Required total = 5 × 16 = 80. Known total = 65. The missing number is 15.
Quick method: Check whether a graph scale increases in ones, twos, fives or another interval.
Question 5 of 10 Mathsexam-styleThe temperatures are −3°C, 4°C, −1°C, 6°C and 9°C. What is the range?
- A6°C
- B9°C
- C10°C
- D12°C
Need a hint?
The distance from a negative minimum to a positive maximum crosses zero.
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Answer D: 12°C
9 − (−3) = 12°C.
Quick method: Check whether a graph scale increases in ones, twos, fives or another interval.
Question 6 of 10 MathscoreFind the mean of 6, 8, 9, 12 and 15.
- A9
- B9.5
- C10
- D12
Need a hint?
Add all five values, then divide by five.
Show worked answer
Answer C: 10
The total is 50; 50 ÷ 5 = 10.
Quick method: Check whether a graph scale increases in ones, twos, fives or another interval.
Question 7 of 10 MathscoreWhat is the range of 14, 7, 19 and 11?
- A5
- B8
- C10
- D12
Need a hint?
Subtract the smallest value from the largest.
Show worked answer
Answer D: 12
19 − 7 = 12.
Quick method: Check whether a graph scale increases in ones, twos, fives or another interval.
Question 8 of 10 MathscoreFind the median of 12, 3, 14, 8 and 7.
- A8
- B7
- C9
- D12
Need a hint?
Put the values in order first.
Show worked answer
Answer A: 8
In order they are 3, 7, 8, 12, 14. The middle value is 8.
Quick method: Check whether a graph scale increases in ones, twos, fives or another interval.
Question 9 of 10 MathsexamOn a bar chart, each grid square represents 4 pupils. One bar is 7 squares high and another is 11 squares high. What is the difference?
- A4 pupils
- B16 pupils
- C18 pupils
- D44 pupils
Need a hint?
Find the difference in grid squares before applying the scale.
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Answer B: 16 pupils
The bars differ by 4 squares; 4 × 4 pupils = 16 pupils.
Quick method: Check whether a graph scale increases in ones, twos, fives or another interval.
Question 10 of 10 MathsstretchThe mean of five numbers is 18. When the number 24 is removed, what is the mean of the remaining four numbers?
- A15
- B16
- C16.5
- D17
Need a hint?
Use the original mean to find the original total.
Show worked answer
Answer C: 16.5
The original total is 5 × 18 = 90. Removing 24 leaves 66; 66 ÷ 4 = 16.5.
Quick method: Check whether a graph scale increases in ones, twos, fives or another interval.